索伯列夫空间中的有界线性算子的最佳逼近

讨论索伯列夫空间H0^2[a，b]中的有界线性算子的最佳逼近问题，利用此空间中的再生核给出了最佳逼近算子的具体表达形式，并且给出了最佳逼近算子的收敛性的结论．     

非线性时滞系统自适应模糊动态面控制

针对未知非线性系统控制器设计过程中引入逼近器过多的问题,提出一种简化的自适应模糊动态面控制器设计方案.在控制器设计过程中,仅采用一个模糊逻辑系统作为逼近器,使得所有的未知项得到补偿,同时采用自适应技术在线辨识未知参数和逼近误差上界.文中的控制方案克服了传统backstepping控制器中"复杂性膨胀"的问题.通过构造合适的Lyapunov函数,证明闭环系统的所有信号为半全局最终一致有界.仿真实例验证所提出的控制方案的有效性.     

具有函数的泛逼近性能的模糊控制器的设计

构造出9类具有函数的泛逼近性能的模糊控制器,这些模糊控制器均由模糊蕴涵算子构造而成.利用倒车仿真说明采用具有函数的泛逼近性能的模糊控制器可以用于实际的模糊控制系统中.     

一类MIMO非线性系统的稳定自适应模糊控制

针对一类 MIMO不确定非线性系统 ,基于一种修改的李亚普诺夫函数并利用 I型模糊系统的逼近能力 ,提出一种分散自适应模糊控制器设计的新方案。该方案不但能够避免现有的一些自适应模糊 /神经网络控制器设计中对控制增益一阶导数上界的要求 ,而且能够避免控制器的奇异问题。通过理论分析 ,证明闭环控制系统是全局稳定的 ,跟踪误差收敛到零。仿真结果表明了该方法的有效性。     

在W2^1（R）空间中函数逼近的一种新方法

在再生核空间W2^1(R)中，利用再生核的性质实现了既不用计算导数也不需要计算积分，而只用函数值就可以将函数展开成级数的一种方法，并且这种级数的部分和{fn(x)}作为逼近f(x)的序列，它的误差rn(x)=f(x)-fn(x)在空间范数意义下单调下降．     

模糊系统及其通用性

本文应用Ｓｔｏｎｅ－Ｗｅｉｅｒｓｔｒａｓｓ定理证明了一类结构为普遍的模糊系统可以任意精度上逼近一实连函数。文章最后也证明了以此系统构成的模糊控制器是通用控制器。     

三层前向神经网络的一致逼近性

近年来，前向神经网络泛逼近的一致性分析一直为众多学者所重视。本文系统分析三层前向网络对于拟差值保序函数族的一致逼近性，其中，转换函数σ是广义Sigmoidal函数。并将此一致性结果用于建立一类新的模糊神经网络(FNN)，即折线FNN．研究这类网络对于两个给定的模糊函数的逼近性，相关结论在分析折线FNN的泛逼近性时起关键作用。     

一类模糊互联系统的新时滞依赖稳定性条件

针对一类连续模糊定常时滞互联系统,提出了一种模糊分散控制器的控制方法,给出了新的时滞依赖稳定性条件.应用Lyapunov函数法,自由权重矩阵,及线性矩阵不等式(LMIs)方法证明了模糊分散控制系统稳定.仿真结果进一步验证了所提出模糊分散控制方法的有效性.     

多项式核最小二乘正则化回归的逼近阶

给出具有多项式核最小二乘正则化回归算法的逼近阶, 目的是解决学习理论中回归问题的误差分析. 构造了一种可以产生逼近于最优逼近阶的正则化方案, 而所得到的逼近阶依赖于多项式空间的维数和具有多项式核的再生核Hilbert 空间, 同时也建立了Borel 概率测度下的~$L_{\rho_X}^2$ 空间中Bernstein-Durrmeyer 算子逼近的正定理.     

模糊映射的完全广义混合型强变分不等式

研究关于模糊映射的一类新的变分不等式－模糊映射的完全广义混合型强变分不等式,得到此类变分不等式解的存在定理分解的一个逼近算法,推广了文[4]和文[8]的主要结果。     

One Machine Scheduling Problem with Fuzzy Random Due-Dates

In many classical or basic scheduling models, jobs processing times and due-dates are crisp values. Recently, they have been formulated as uncertain values in some more actual models. That is the introduction of fuzziness. However, in a real situation of decision making, there exists uncertainty that can not be described only by fuzziness. In this paper, we propose an n-job, one machine scheduling model, where due-dates for jobs are fuzzy random variables. In the model, jobs processing times are crisp, and we assign satisfaction levels to jobs completion times according to membership functions. They are non-increasing functions, but their support positions depend upon the expected due-dates, which are exponentially distributed random variables.     

一个最优的模糊逼近器

In a dot product space with the reproducing kernel (r. k. S. ) ,a fuzzy system with the estimation approximation errors is proposed ,which overcomes the defect that the existing fuzzy control system is difficult to estimate the errors of approximation for a desired function,and keeps the characteristics of fuzzy system as an inference approach. The structure of the new fuzzy approximator benefits a course got by other means.     

基于观测器的模糊Delta算子系统的控制器设计

对于非线性模糊系统控制器和观测器的分析和设计,提出一种统一方法。利用Delta域离散T—S模糊模型对非线性系统建模,并基于李雅普诺夫稳定性理论给出模糊状态反馈控制器和观测器的设计策略,将所得结果归结为求解一组线性矩阵不等式。同时结论表明:分离性原理对Delta算子T—S模糊系统仍然成立。所得结果可将现有关于连续和离散T—S模糊系统的相关结论统一于Delta算子框架内。     

Fuzzy delayed output feedback synchronization for time-delayed chaotic systems

In this paper, we propose a new fuzzy delayed output feedback synchronization (FDOFS) method for time-delayed chaotic systems. Based on Lyapunov–Krasovskii theory, T–S fuzzy model, and delayed feedback control scheme, the FDOFS controller is designed and an analytic expression of the controller is shown. The proposed controller can guarantee asymptotical synchronization of both drive and response systems. The FDOFS controller can be obtained by solving the linear matrix inequality (LMI) problem. A numerical example for time-delayed Lorenz system is presented to demonstrate the validity of the proposed FDOFS method.     

RELATIVE COMPACTNESS AND COMPACTNESS OF GENERAL SUBSETS IN AN I- TOPOLOGICAL SPACE

Abstract

In a previous work, we introduced a form of compactness applicable to general fuzzy sets in an I-topological space. It was shown that many of the standard results for compactness in general topology remain valid in the fuzzy setting. In this paper we continue our investigations into the behaviour of compact fuzzy subsets. We also introduce the notion of a relatively compact fuzzy subset and obtain results very similar to those of general topology. Many of our results are in the setting of fuzzy neighbourhood space and fuzzy uniform spaces. In particular, a number of criteria for compactness, already known for the whole space, are extended to arbitrary fuzzy subsets in a fuzzy neighbourhood space.     

A new hybrid algorithm based on optimal fuzzy controller in multimachine power system

In this article, a new methodology based on fuzzy proportional‐integral‐derivative (PID) controller is proposed to damp low frequency oscillation in multimachine power system where the parameters of proposed controller are optimized offline automatically by hybrid genetic algorithm (GA) and particle swarm optimization (PSO) techniques. This newly proposed method is more efficient because it cope with oscillations and different operating points. In this strategy, the controller is tuned online from the knowledge base and fuzzy interference. In the proposed method, for achieving the desired level of robust performance exact tuning of rule base and membership functions (MF) are very important. The motivation for using the GA and PSO as a hybrid method are to reduce fuzzy effort and take large parametric uncertainties in to account. This newly developed control strategy mixed the advantage of GA and PSO techniques to optimally tune the rule base and MF parameters of fuzzy controller that leads to a flexible controller with simple structure while is easy to implement. The proposed method is tested on three machine nine buses and 16 machine power systems with different operating conditions in present of disturbance and nonlinearity. The effectiveness of proposed controller is compared with robust PSS that tune using PSO and the fuzzy controller which is optimized rule base by GA through figure of demerit and integral of the time multiplied absolute value of the error performance indices. The results evaluation shows that the proposed method achieves good robust performance for a wide range of load change in the presents of disturbance and system nonlinearities and is superior to the other controllers. © 2014 Wiley Periodicals, Inc. Complexity 21: 78–93, 2015     

A self-organizing adaptive fuzzy controller

There are two main parts in this paper. The first part presents a knowledge representation and reasoning scheme, called tree-searched neural networks (TNN). The TNN is based on a well-known intuitive knowledge representation (IKR) and can reduce the number of the processing nodes in the neural networks. The second part proposes a self-organizing adaptive fuzzy controller (SOAFC) based on the TNN model. It can help acquire control knowledge and thus can reduce the dependence on experts. Furthermore, designers do not need to predefine all membership functions to cover whole input space domain. For improving its performance further, we design a D-controller which is included within the SOAFC. Whether the fuzzy controller is incorporated with the D-controller or not, it is also guaranteed to be globally stable. Simulation results show that this approach has faster convergence speed, results in better transient response, and in addition requires less total control energy.     

Fuzzy guaranteed cost controller for trajectory tracking in nonlinear systems

In this paper, we propose a fuzzy logic based guaranteed cost controller for trajectory tracking in nonlinear systems. Takagi–Sugeno (T–S) fuzzy model is used to represent the dynamics of a nonlinear system and the controller design is carried out using this fuzzy model. State feedback law is used for building the fuzzy controller whose performance is evaluated using a quadratic cost function. For designing the fuzzy logic based controller which satisfies guaranteed performance, linear matrix inequality (LMI) approach is used. Sufficient conditions are derived in terms of matrix inequalities for minimizing the performance function of the controller. The performance function minimization problem with polynomial matrix inequalities is then transformed into a problem of minimizing a convex performance function involving standard LMIs. This minimization problem can be solved easily and efficiently using the LMI optimization techniques. Our controller design method also ensures that the closed-loop system is asymptotically stable. Simulation study is carried out on a two-link robotic manipulator tracking a reference trajectory. From the results of the simulation study, it is observed that our proposed controller tracks the reference trajectory closely while maintaining a guaranteed minimum cost.     

自组织结构的变论域模糊控制

针对变论域模糊控制,提出一种新的自组织结构的变论域模糊控制方法。自组织结构算法可以调整变论域模糊系统结构以及动态获得模糊规则,进一步减小变论域模糊控制项的稳态逼近误差。通过进一步理论分析可知,自组织结构算法仅仅保证了系统瞬时的切换是平稳的,但不能保证系统的闭环稳定性。给出了所提出控制方法的适用条件。通过与固定模糊系统结构的变论域模糊控制比较,仿真结果表明,所提出控制方法不仅使得系统的稳态跟踪误差更平稳,而且使得输入控制信号更加平滑。     

A general fuzzy control scheme for nonlinear processes with stability analysis

In this paper we develop a general fuzzy control scheme for nonlinear processes. Assuming little knowledge about the dynamics of the controlled process, the proposed scheme starts by probing the process at different points in its operating region to generate a fuzzy quantisation. A simple local controller is then designed at each fuzzy locality. A fuzzy inference mechanism then links up tje local controllers to form a global controller which can be further refined by the learning algorithm. By employing a newly developed structure-adaptive fuzzy modelling scheme, the appropriate fuzzy rule-base for the inference mechanism can be extracted stably and efficiently. The conditions for the stability of the global controller are rigourously established. Simulation results are presented to illustrate the effectiveness of the scheme.